Fourier series and approximation on hexagonal and triangular domains

TL;DR

This paper explores Fourier series and approximation techniques on hexagonal and triangular domains, establishing summability, approximation degrees, and theoretical foundations for spectral set Fourier expansions.

Contribution

It develops a comprehensive theory for Fourier series on spectral sets like hexagons and triangles, including summability and approximation results.

Findings

Abel and Cesàro summability established for Fourier series

Degree and best approximation by trigonometric functions analyzed

Inverse and direct approximation theorems proved

Abstract

Several problems on Fourier series and trigonometric approximation on a hexagon and a triangle are studied. The results include Abel and Ces\`aro summability of Fourier series, degree of approximation and best approximation by trigonometric functions, both direct and inverse theorems. One of the objective of this study is to demonstrate that Fourier series on spectral sets enjoy a rich structure that allow an extensive theory for Fourier expansions and approximation.